So I'm not crazy. Every epi/gibby I've owned refuses to have an in-tune G string. Strat hangs on the wall for months and is still in tune.
I dont know if it's been mentioned, but the reason for this is the headstock tilt and the the angle that the strings break away from the nut to the tuning pegs. The headstock needs a slight tilt so that the strings produce a note at the nut. Too much of a tilt, too thick of a string, or too much of an angle towards the tuning pegs can all cause the string to bind and catch on the nut and cause an out of tune note. This is especially true with non-locking trems and its also why floyd rose's stay in tune so well- there is nowhere for the string to slip. If there is no locking nut, locking tuners, in my opinion, are essential because the string cant become ever-so-slightly unwound on the tuning peg and go out of tune. Also guitars where the string is a perfectly straight line from the bridge to the tuning peg with only a slight headstock tilt will pretty much always stay in tune better. Also the construction, neck material, and truss rod stability. can have an effect. The more stable the construction and the harder the wood, the better it will stay in tune.